Correlation propagation for uncertainty analysis of structures based on a non-probabilistic ellipsoidal model.

• Correlation propagation method is proposed to obtain the uncertain responses domain. • The ME model is utilized to quantify the uncertainties in parameters and responses. • Subinterval decomposition analysis method is adopted to evaluate response intervals. • The non-probabilistic correlation propagation equations are theoretically derived. • The propagated correlations are completely accurate for the second-order systems. Traditional non-probabilistic methods for uncertainty propagation problems evaluate only the lower and upper bounds of structural responses, lacking any analysis of the correlations among the structural multi-responses. In this paper, a new non-probabilistic correlation propagation method is proposed to effectively evaluate the intervals and non-probabilistic correlation matrix of the structural responses. The uncertainty propagation process with correlated parameters is first decomposed into an interval propagation problem and a correlation propagation problem. The ellipsoidal model is then utilized to describe the uncertainty domain of the correlated parameters. For the interval propagation problem, a subinterval decomposition analysis method is developed based on the ellipsoidal model to efficiently evaluate the intervals of responses with a low computational cost. More importantly, the non-probabilistic correlation propagation equations are newly derived for theoretically predicting the correlations among the uncertain responses. Finally, the multi-dimensional ellipsoidal model is adopted again to represent both uncertainties and correlations of multi-responses. Three examples are presented to examine the accuracy and effectiveness of the proposed method both numerically and experimentally. [ABSTRACT FROM AUTHOR]